The Qur'an doesn't exclude any type of fish. It simply says that meat from the sea is lawful:
Lawful to you is game from the sea and its food as provision for you and the travelers, but forbidden to you is game from the land as long as you are in the state of ihram. And fear Allah to whom you will be gathered. 5:96
And it is He who subjected the sea for you to eat from it tender meat and to extract from it ornaments which you wear. And you see the ships plowing through it, and [He subjected it] that you may seek of His bounty; and perhaps you will be grateful. 16:14
And not alike are the two bodies of water. One is fresh and sweet, palatable for drinking, and one is salty and bitter. And from each you eat tender meat and extract ornaments which you wear, and you see the ships plowing through [them] that you might seek of His bounty; and perhaps you will be grateful.35:12
The idea that bottom feeders are not considered halal is because people concluded that its behavior is similar to swine, and thus we should not eat it. This idea is a biddat, to belive that it is haram, when Allah and the sunnah of the prophet (pbuh) have made it permissible for us.
But of course the original ruling for food would still apply:
forbidden to you is that which dies of itself, and blood, and flesh of swine, and that on which any other name than that of allah has been invoked, and the strangled (animal) and that beaten to death, and that killed by a fall and that killed by being smitten with the horn, and that which wild beasts have eaten, except what you slaughter, and what is sacrificed on stones set up (for idols) and that you divide by the arrows; that is a transgression. this day have those who disbelieve despaired of your religion, so fear them not, and fear me. this day have i perfected for you your religion and completed my favor on you and chosen for you islam as a religion; but whoever is compelled by hunger, not inclining willfully to sin, then surely allah 5:3
As for slaughtering it yourself and invoking Allah's name, the hadith you quoted above already explains that meat from the sea is already slaughtered correctly.